Govindarajulu / Birnbaum / Lukacs Sequential Statistical Procedures

1. Auflage 2014
ISBN: 978-1-4832-6332-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 584 Seiten, Web PDF

Probability and Mathematical Statistics, Volume 26: Sequential Statistical Procedures provides information pertinent to the sequential procedures that are concerned with statistical analysis of data. This book discusses the fundamental aspects of sequential estimation. Organized into four chapters, this volume begins with an overview of the essential feature of sequential procedure. This text then examines the sequential probability ratio test procedure and provides a method of constructing a most powerful test for a simple hypothesis versus simple alternative-testing problem. Other chapters consider the problem of testing a composite hypothesis against a composite alternative. This book discusses as well the theory of sequential tests that is appropriate for distinguishing between two simple or composite hypotheses. The final chapter deals with the theory of sequential estimation. This book is a valuable resource for graduate students, research workers, and users of sequential procedures.

Autoren/Hrsg.

Govindarajulu, Z.

Birnbaum, Z. W.

Lukacs, E.

Inhaltsverzeichnis

1;Front Cover;1
2;Sequential Statistical Procedures;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Preface;12
7;Notation;14
8;CHAPTER 1. Introduction and Certain Double
Sampling Procedures;18
8.1;1.1 Introduction to Sequential Testing;18
8.2;1.2 Sampling Inspection;20
8.3;1.3 Loss and Risk Functions;23
8.4;1.4 Certain Double Sampling Procedures;24
9;CHAPTER 2. The Sequential Probability
Ratio Test;31
9.1;2.1 The Sequential Probability Ratio Test (SPRT);31
9.2;2.2 Finite Termination of the SPRT;40
9.3;2.3 The Operating Characteristic Function
(OC Function);42
9.4;2.4 Average Sample Number;45
9.5;2.5 Wald's Fundamental Identity;57
9.6;2.6 Bounds for the Expected Sample Size in a SPRT;71
9.7;2.7 Formulas for Calculating the Operating Characteristic and
the Average Sample Number of Some Sequential Tests;84
9.8;2.8 Truncated SPRT;93
9.9;2.9 Optimal Properties of the SPRT;95
9.10;2.10 Generalized SPRT (GSPRT);104
9.11;2.11 Restricted SPRT;106
9.12;2.12 Extended SPRTs;110
9.13;2.13 Asymptotic Properties of SPRTs;114
10;CHAPTER 3. Sequential Tests for Composite
Hypotheses;118
10.1;3.1 Wald's (1947) Method of Weight Functions;118
10.2;3.2 Sequential t- and t2- Tests and Sequential
Analogues of Stein's Two-Stage Test;120
10.3;3.3 Sequential F-Test;136
10.4;3.4 Certain Two-Sample Sequential Procedures;138
10.5;3.5 Fraser Sufficiency and Conditional Tests;140
10.6;3.6 Invariant Sequential Procedures;143
10.7;3.7 Sequential Likelihood Ratio Test Procedures;164
10.8;3.8 Sequential Tests Between Three Hypotheses;180
10.9;3.9 Sequential
k-Decision Problems;192
10.10;3.10 Sequential Tests for Two-Sided Alternatives;212
10.11;3.11 Efficiency of the SPRT;226
10.12;3.12 Bayes Sequential Procedures;244
10.13;3.13 Iterated Logarithm Inequalities and Their Application
to Sequential Testing Hypotheses;261
10.14;3.14 Certain Nonparametric Sequential Test Procedures;270
10.15;3.15 Locally Most Powerful (LMP) Sequential Tests;301
11;CHAPTER 4. Sequential Estimation;310
11.1;4.1 Introductory Remarks;310
11.2;4.2 Certain Two-Stage Procedures;310
11.3;4.3 Formulation of the Problem of Sequential Estimation
by Intervals or Sets;332
11.4;4.4 Wald's Sequential Estimation Procedures;333
11.5;4.5 Certain General Concepts of Sequential Estimation;334
11.6;4.6 Cramér-Rao Lower Bound for the Sequential Case;334
11.7;4.7 Sufficiency and Completeness in the Sequential Case;339
11.8;4.8 Minimax Estimation;349
11.9;4.9 A Class of Situations Where Bayes Sequential Estimation
Procedure Is Nonsequential;360
11.10;4.10 Sequential Estimation and Certain Closed Sequential Decision
Procedures;375
11.11;4.11 Estimation by Double Sampling;384
11.12;4.12 Large Sample Theory of Sequential Estimation;394
11.13;4.13 Sequential Confidence Intervals for the Mean of a Normal
Population with Unknown Variance;402
11.14;4.14 The Asymptotic Theory of Fixed-Width Sequential Confidence
Intervals for the Mean;429
11.15;4.15 Asymptotic Theory of Fixed-Size Sequential Confidence Bounds
for Linear Regression Parameters;445
11.16;4.16 Confidence Sequences for Other Parameters;452
11.17;4.17 Sequential Estimation of the Mean Vector of a Multivariate
Normal Distribtuion;469
11.18;4.18 A General Method of Determining Fixed-Width
Confidence Intervals;481
11.19;4.19 Sequential Estimation of the Size of a Finite Population;487
11.20;4.20 Consistency of Certain Sequential Estimators;492
11.21;4.21 Asymptotically Optimal Bayes Sequential Estimation;499
11.22;4.22 Sequential Nonparametric Confidence Intervals for Certain
Parameters of the Population;504
11.23;4.23 Certain Problems of Optimal Stopping;521
12;APPENDIX 1: Solution to Wald's liquation;530
13;APPENDIX 2: Differentiation of an Expectation;532
14;APPENDIX 3: On the Moments of a Random
Variable;535
15;APPENDIX 4: The Normal Diffusion Process;537
16;APPENDIX 5: Large Sample Properties of
Maximum Likelihood estimates;544
17;APPENDIX 6: A Table of Standard Distributions;547
18;APPENDIX 7: A Useful Convergence Theorem
of Cramer;549
19;APPENDIX 8: Backward Induction;551
20;References and Author Index;554
21;Subject Index;572
22;Probability and Mathematical Statistics;584